curve #885

y² + xy + y = x³ − x² − x − 14

a-invariants: [1, -1, 1, -1, -14]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 17
discriminant (Δ): -83521
Faltings height: -0.3766
naive height: 18.7878
primes of bad reduction: 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:55:01 UTC
last updated: 2026-09-23 14:55:01 UTC

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Commentary

Cremona 17a1 = LMFDB 17.a3: https://www.lmfdb.org/EllipticCurve/Q/17/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 17, minimal discriminant -83521, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 14:55:01 UTC · history